The impact of covariates on a bonus–malus system: an application of Taylor’s model

Abstract

Obviously, the design of a bonus–malus system has to take into consideration all rating variables used by the auto insurance carrier. For instance, a single male urban driver is likely to be penalized twice, a priori through explicit surcharges linked to his risk class, and a posteriori through premium increases triggered by the transition rules of the bonus–malus system, creating the possibility of excessive premiums through double-counting for the same reason. Taylor (ASTIN Bull 27:319–327, 1997) developed a Bayesian model to evaluate the impact of covariate rating variables on bonus–malus premium levels, but could not access actual data to implement his model. We present the first real-life application of Taylor’s research, by using a unique database originating from Taiwan and the bonus–malus system in force in this island. Our data combines car and insurance information from the leading insurer in the island with annual mileage readings from a network of repair shops operated by the largest car manufacturer—over a quarter million policy-years. Park et al. (The use of annual mileage as a rating variable. Working paper, 2014), using the same data, used negative binomial regression to prove that mileage is by far the best predictor of accidents. The application of Taylor’s model concludes that the impact of mileage on bonus–malus premium levels is small. Therefore, double-counting should not be considered as a major concern in practice.